This is a hard thing to do. I am an exchange student from the States, and I just had to bring my bike with me. Obviously, Denmark is lacking in the "mountain" department, but not in the public, worthy, off-road trail department. These trails range from technical singletrack to fireroads. There is a nice bit of climbing there, oddly, but that means that downhills are available. You must be willing to explore a bit, and these trails will not disappoint. They are criss-crossed with equestrian and hiking trails, and since the Danes are usually very active, be ready to see people. Very rarely do the trails take the same route, so you will be able to be less mindful of spooking a horse most of the time.